Multilevel Statistical Models and Ecological Scaling

Berk, Richard A.; Leeuw, Jan de

doi:10.1007/1-4020-4663-4_4

Cited by 5 publications

(6 citation statements)

References 15 publications

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“…There exists predictive performance with a higher bias for the whole dataset than the sub-datasets (i.e., data from different climate regimes) for linear regression approach. Therefore, to improve our understanding for baseflow processes and BFI prediction, the interaction of catchment attributes within different climate zones should be considered (Berk and De Leeuw, 2006).…”

Section: Linear Regression Approachmentioning

confidence: 99%

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Large-scale baseflow index prediction using hydrological modelling, linear and multilevel regression approaches

Zhang

Song

et al. 2020

Journal of Hydrology

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Section: Linear Regression Approachmentioning

confidence: 99%

“…It provides a robust tool to establish the relationships between BFI and catchment attributes. The basic idea of this approach is that higher-level variables vary within lower-level variables (Berk and De Leeuw, 2006). This approach can also handle the variables with various solutions using hierarchical structure (Dudaniec et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Large-scale baseflow index prediction using hydrological modelling, linear and multilevel regression approaches

Zhang

Song

et al. 2020

Journal of Hydrology

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“…Moreover, in addition to illustrating the importance of incorporating scales when modeling associations in ecological systems, HLM development and diagnostics provide a complex yet accessible means of studying populations, communities and ecosystems (McMahon and Diez 2007). In recent years, HLM has been applied to ecological studies of community interaction (Vázquez and Simberloff 2004), species-area relationships (Storch et al 2005), habitat covariates in species count data (Thogmartin et al 2006;Dêschenes and Rodriguez 2007), age-dependent reproduction (Van de Pol and Verhulst 2006), spatial covariance (Berk and de Leeuw 2006), herbivore damage (McMahon and Diez 2007) and reef-fish metacommunity structures (MacNeil et al 2009). These studies demonstrate that ecological applications of HLM can benefit from an analysis protocol that constructs models with a clear concept of the role of scale in a system, and utilizes them to analyze important diagnostic measures of variation and association (McMahon and Diez 2007).…”

Section: Introductionmentioning

confidence: 99%

Monitoring and estimating scale-dependent hierarchical relationships between Sicyopterus japonicus density and stream habitat features in different seasons in northern Taiwan

Lin

Wang

2011

Environ Monit Assess

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Biological and physical processes operate collaboratively through spatial or temporal scales to form ecological patterns, which are considered as a key element for understanding the natural liens within an ecosystem. Given the importance of scaling in ecological inference, this study elucidates how physical and biological variables under or within scales interact with each other. Density of Sicyopterus japonicus and environmental variables are examined and quantified at 70 stream sections distributed among 14 reaches in the Datuan stream catchment of northern Taiwan during the fall and winter of 2007, as well as the spring and summer of 2008. Hierarchical linear regression analysis indicates that S. japonicus density and habitat features are related on two levels, i.e., sections within reaches and reaches within streams throughout the year. Moreover, parameter uncertainty is represented by the confidence interval, which is calculated by the variance-covariance matrix of hierarchical linear model (HLM) parameters. According to HLM results, environmental variables at the section level (water depth and current velocity) and the reach level (stream width, water temperature, stream slope, soil erosion index) influence S. japonicus density. Although S. japonicus density varies significantly among reaches and sections within reaches, cross-level interaction may not always influence the distribution, processes and activities of S. japonicus throughout the year. The HLMs of S. japonicus density associated with stream features describe thoroughly multiple processes and the activities of S. japonicus across scales and within scales during different seasons. The annual HLM results represent the overall biological and physical patterns of the Datuan stream annually, explaining why they do not reflect seasonal associations or explain S. japonicus-related activities and environmental features of the stream.

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“…Results and predictions can be communicated across systems and research programmes. HLM has been applied to ecological problems related to community interactions (Vazquez & Simberloff 2004), species-area relationships (Storch et al 2005), habitat covariates in species count data (Thogmartin et al 2006), age-dependent reproduction (van de Pol & Verhulst 2006) and spatial covariance (Gering & Crist 2002;Berk & de Leeuw 2006). Applications of HLM in ecology, however, can benefit from a protocol of analysis that builds models towards a clear concept of the role of scale in a system, and incorporate into the analysis important diagnostic measures of variation and association.…”

Section: Introductionmentioning

confidence: 99%

“…2005), habitat covariates in species count data (Thogmartin et al. 2006), age‐dependent reproduction (van de Pol & Verhulst 2006) and spatial covariance (Gering & Crist 2002; Berk & de Leeuw 2006). Applications of HLM in ecology, however, can benefit from a protocol of analysis that builds models towards a clear concept of the role of scale in a system, and incorporate into the analysis important diagnostic measures of variation and association.…”

Section: Introductionmentioning

confidence: 99%

Scales of association: hierarchical linear models and the measurement of ecological systems

2007

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A fundamental challenge to understanding patterns in ecological systems lies in employing methods that can analyse, test and draw inference from measured associations between variables across scales. Hierarchical linear models (HLM) use advanced estimation algorithms to measure regression relationships and variance-covariance parameters in hierarchically structured data. Although hierarchical models have occasionally been used in the analysis of ecological data, their full potential to describe scales of association, diagnose variance explained, and to partition uncertainty has not been employed. In this paper we argue that the use of the HLM framework can enable significantly improved inference about ecological processes across levels of organization. After briefly describing the principals behind HLM, we give two examples that demonstrate a protocol for building hierarchical models and answering questions about the relationships between variables at multiple scales. The first example employs maximum likelihood methods to construct a two-level linear model predicting herbivore damage to a perennial plant at the individual- and patch-scale; the second example uses Bayesian estimation techniques to develop a three-level logistic model of plant flowering probability across individual plants, microsites and populations. HLM model development and diagnostics illustrate the importance of incorporating scale when modelling associations in ecological systems and offer a sophisticated yet accessible method for studies of populations, communities and ecosystems. We suggest that a greater coupling of hierarchical study designs and hierarchical analysis will yield significant insights on how ecological processes operate across scales.

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Multilevel Statistical Models and Ecological Scaling

Cited by 5 publications

References 15 publications

Large-scale baseflow index prediction using hydrological modelling, linear and multilevel regression approaches

Large-scale baseflow index prediction using hydrological modelling, linear and multilevel regression approaches

Monitoring and estimating scale-dependent hierarchical relationships between Sicyopterus japonicus density and stream habitat features in different seasons in northern Taiwan

Scales of association: hierarchical linear models and the measurement of ecological systems

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